--- product_id: 2521578 title: "Set Theory (Studies in Logic: Mathematical Logic and Foundations)" brand: "kenneth kunen" price: "£34.92" currency: GBP in_stock: true reviews_count: 8 url: https://www.desertcart.co.uk/products/2521578-set-theory-studies-in-logic-mathematical-logic-and-foundations store_origin: GB region: United Kingdom --- # Set Theory (Studies in Logic: Mathematical Logic and Foundations) **Brand:** kenneth kunen **Price:** £34.92 **Availability:** ✅ In Stock ## Quick Answers - **What is this?** Set Theory (Studies in Logic: Mathematical Logic and Foundations) by kenneth kunen - **How much does it cost?** £34.92 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.co.uk](https://www.desertcart.co.uk/products/2521578-set-theory-studies-in-logic-mathematical-logic-and-foundations) ## Best For - kenneth kunen enthusiasts ## Why This Product - Trusted kenneth kunen brand quality - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Description Set Theory (Studies in Logic: Mathematical Logic and Foundations) ## Images ![Set Theory (Studies in Logic: Mathematical Logic and Foundations) - Image 1](https://m.media-amazon.com/images/I/41LlXo1ac6L.jpg) ![Set Theory (Studies in Logic: Mathematical Logic and Foundations) - Image 2](https://m.media-amazon.com/images/I/519tYaN0B7L.jpg) ![Set Theory (Studies in Logic: Mathematical Logic and Foundations) - Image 3](https://m.media-amazon.com/images/I/31Gy8Bm6O9L.jpg) ## Customer Reviews ### ⭐⭐⭐⭐ The 2011 successor to Kunen's 1980 set theory book *by N***E on Reviewed in the United States on June 22, 2012* INITIAL REVIEWThis will be a short initial review prior to reading any of this very recently acquired book. This book by master expositor Kenneth Kunen, emeritus at University of Wisconsin-Madison, is a newly rewritten 2011 update of his well regarded, rather standard 1980 edition, still available at  Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics) . In Professor Kunen's short new preface, he cites two reasons why the new edition was needed, 1) more set theory has been discovered in the past 30 years, especially related to Martin's Axiom. 2) model theoretic methods are far more more known and used than in 1980. Another plus of this new edition is that it is published in a decent quality, but inexpensive College Publications paperback imprint. I've been handling this book a lot for over a month so far and the paper cover is still flat and undamaged.Long chapter I called 'Background Material' is rather similar to great chapter I on ZFC set theory in Kunen's excellent 2009 book  The Foundations of Mathematics (Logic S.) , which I have read thru 100 page chapter II on model theory and proof theory, with chapter II twice, and finally read short chapter III on philosophy of math. There is a huge review from this reader on the page for that foundations book.BASIC BOOK CONTENTS: Preface-v / 0 Introduction-1 / I Background Material-5 / II Easy Consistency Proofs-106 / III Infinitary Combinatorics-153 / IV Forcing-243 / V Iterated Forcing-314 / Bibliography-388 / Indices-395 (both symbols and subjects) // As in the foundations book, the indexes in this book are really tiny and inadequate. This is again mitigated by Kunen's very effective constant cross-referencing ahead, but mostly behind, and I've found the back-references to be very helpful to my reading. Looking back at contents of the previous edition, which I do not own, that WAS quite a different book than this new one is.READING IN THIS BOOKCHAPTER I / GENERAL COMMENTSRead chapter 0 and started long chapter I on Tue 31Jul12. One thing that strikes me in both of these CP books by Ken Kunen is how involving and insightful he is as a writer. There tends to be a big motivation to keep reading these books. Finished great chap I section 6 on relations and functions on Tue 7Aug12 afternoon, so onward to ordinals next. One improvement in chapter I of this set theory book over chapter I in Kunen's foundations book is perhaps a bit clearer version of getting right into business in the present read, making it a 'smoother' read. Another difference in the chapter 1s is that in this book, he covers a few more subjects than in the other one, so there is less coverage of general set theoretical subjects.Finished both very good sections on ordinals Thu 9Aug12 afternoon. Next section I.9 on 'Induction and Recursion and Foundation' is a large 22 pages long, so that should be a good, long read. Section 9 is appearing to be just way full of Kunen's best wise insights, a real joy to read! One thing that seems to apply mainly in chapter I of this book is that many proofs are skipped, or short proofs are written more in a suggestive way, as if that proof, in an unspoken way, is really the student's job. This bad practice continues in chapter II of this book. For comparison, chapter I of the foundations book contains more thorough proofs of many of the missing or cursory proofs in the present book. Therefore, ideally, a reader should get both of these inexpensive books by professor Kunen, as they are mostly complementary. For example 100 page chapter II of foundations gives an excellent large hit of model theory, which is only touched on in late chapter I of the present book, but model theory is used extensively later in this book.Excellent nuggets of wisdom continue. Finally finished long section I.9 on Mon 20Aug12 and soon read short and interesting I.10 and I.11 on cardinalities. I.12 on the Axiom of Choice and its equivalent statements was especially interesting, ending on p. 72 and finished on Fri 24Aug12. Long I.13 on cardinal arithmetic is nearly the same as I.13 of the foundations book. Tedious going thru this difficult section a second time. Finished I.13, read short I.14 on identity of mathematical objects, and started moderately long I.15 on model theory Mon 27Aug12, going to p. 84. Section I.16 on models for set theory looks forward quite a bit to the work in rapidly upcoming chapter II. Finished I.16, very short I.17 on recursion theory, and whole chapter I Wed 5Sep12 mid day.CHAPTER IIRead thru somewhat informal and short section II.1 on Thu 6Sep12. Longer section II.2 and shorter II.3 will focus on the Foundation Axiom and ends up formally adopting that little-used axiom into this book's WF (well-founded) set theory. That section II.2 is quite interesting and well done. Long section II.4 on 'More on Absoluteness' is some excellent mathematics. The concept of absoluteness was just introduced in section I.16, so here we fill out that theory. Section II.5 on reflection theorems seems to work toward making an end run around some limitations of smaller versions than full ZFC set theory.Following II.5, rather long II.6 on constructible sets was the first one that was brutally difficult for this reader. Murderously difficult definitions and generally hard subjects and symbolism. Skipped most of it, and stopped reading all proofs and exercises/hints during that section. Taking a break from reading this book effective 14:21 Wed 19Sep12. Finished sections II.7 thru II.10 minus exercises, finishing chapter II with my II.6 omissions, etc. on Mon 24Sep12.II.7 was short and vaguely about forcing, while II.8 was about ordinal definable sets and was quite interesting. Then II.9 was strangely about the independence of foundation, which has no effect at all on mathematics. II.10 briefly mentioned set theory with classes as NBG and MK set theories. Kunen has been using proper classes a lot in this book as abbreviations for more complicated logical sentences. ZFC set theory actually contains no proper classes or a universal set, which are strongly used in NBG class-set theory. Here is a book on NBG I have read thru chapter 4:  Set Theory and the Continuum Problem (Dover Books on Mathematics) . Used to have a review of that book for over a year, but deleted it in Aug12, as it seemed to have gone irretrievably bad. In general, chapters in that 1996 Smullyan/Fitting text are awfully short.CHAPTER IIIThis whole chapter on infinitary combinatorics, including Martin's Axiom, is quite difficult to extremely so. At beginning of that chapter, Kunen specifies a total of about 18 of the 90 pages of chapter III for future use, so I will attempt to read that 20% of the chapter before going on to chapter IV on forcing. In total, chapter III contains 8 sections, but recommended reading is in only sections III.1 thru III.3.Started the read in section III.1 Mon 24Sep12 afternoon. The few recommended pages of III.1 feature some really interesting new concepts in cardinals with such cool names as 'meager'/'null'/'non'/'add'/'mad family'. Fascinating section. The only 3 pages of section III.2 deal with topological spaces, and so that is not in my math zone.Section III.3 is a huge 24page section on crucial 'Martin's Axiom' or MA, of which only the first 7 pages are needed. Started that early afternoon on Wed 26Sep12. This is about where things of chapter III start getting more highly difficult. After this chapter III reading, which was finished minus all proofs on Thu 27Sep12, a long time before I just might attempt chapter IV of this book.CHAPTER IVRead good section IV.1, starting chapter IV on forcing mid day on Wed 10Oct12, so we'll see how this chapter goes while reading no proofs or exercises. Gave up continuing in this book after that section IV.1. After chapter II, professor Kunen started writing out much more thorough proofs loaded with more than the usual syntax language symbolic content. That is what makes chapters III and IV appear so very mathematically dense, and for this retired metals guy, dauntingly difficult. Plus, skipping those proofs isn't much of an option, since those proofs are most of the content of these chapters. So this book goes back on my bookshelf. Bye everyone. ### ⭐⭐⭐⭐⭐ Elegant Set Theory Foundations *by T***I on Reviewed in the United States on January 8, 2020* Set theory was one of my favorite areas covered in my Introduction to Advanced Mathematics class. I love the subject and this book does a good job presenting the of the foundations of the area. I can spend all day with this book, I get so much joy from it. It gets its elegance from its simplicity. ### ⭐⭐⭐⭐ Four Stars *by M***A on Reviewed in the United States on October 23, 2015* Good --- ## Why Shop on Desertcart? - 🛒 **Trusted by 1.3+ Million Shoppers** — Serving international shoppers since 2016 - 🌍 **Shop Globally** — Access 737+ million products across 21 categories - 💰 **No Hidden Fees** — All customs, duties, and taxes included in the price - 🔄 **15-Day Free Returns** — Hassle-free returns (30 days for PRO members) - 🔒 **Secure Payments** — Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** — Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.co.uk/products/2521578-set-theory-studies-in-logic-mathematical-logic-and-foundations](https://www.desertcart.co.uk/products/2521578-set-theory-studies-in-logic-mathematical-logic-and-foundations) --- *Product available on Desertcart United Kingdom* *Store origin: GB* *Last updated: 2026-05-16*