Algebra of Proofs deals with algebraic properties of the proof theory of intuitionist first-order logic in a categorical setting. The presentation is based on the confluence of ideas and techniques from proof theory, category theory, and combinatory logic. The conceptual basis for the text is the Lindenbaum-Tarski algebras of formulas taken as categories. The formal proofs of the associated deductive systems determine structured categories as their canonical algebras (which are of the same type as the Lindenbaum-Tarski algebras of the formulas of underlying languages). Gentzen's theorem, which asserts that provable formulas code their own proofs, links the algebras of formulas and the corresponding algebras of formal proofs. The book utilizes the Gentzen's theorem and the reducibility relations with the Church-Rosser property as syntactic tools. The text explains two main types of theories with varying linguistic complexity and deductive strength: the monoidal type and the Cartesian type. It also shows that quantifiers fit smoothly into the calculus of adjoints and describe the topos-theoretical setting in which the proof theory of intuitionist first-order logic possesses a natural semantics. The text can benefit mathematicians, students, or professors of algebra and advanced mathematics.

Frequently asked questions

Simply head over to the account section in settings and click on “Cancel Subscription” - it’s as simple as that. After you cancel, your membership will stay active for the remainder of the time you’ve paid for. Learn more here.

At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.

Both plans give you full access to the library and all of Perlego’s features. The only differences are the price and subscription period: With the annual plan you’ll save around 30% compared to 12 months on the monthly plan.

We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.

Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.

Yes, you can access Algebra of Proofs by M. E. Szabo, K. J. Barwise,D. Kaplan,H. J. Keisler in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher

North Holland

Year

2016

ISBN

9781483275420

Topic

Mathematics

Subtopic

Algebra

Index

Mathematics

Front Cover
Algebra of Proofs
Copyright Page
Table of Contents
Dedication
PREFACE
CHAPTER 1. INTRODUCTION
CHAPTER 2. MONOIDAL CATEGORIES
CHAPTER 3. SYMMETRIC MONOIDAL CATEGORIES
CHAPTER 4. CARTESIAN CATEGORIES
CHAPTER 5. BICARTESIAN CATEGORIES
CHAPTER 6. DISTRIBUTIVE BICARTESIAN CATEGORIES
CHAPTER 7. MONOIDAL CLOSED CATEGORIES
CHAPTER 8. SYMMETRIC MONOIDAL CLOSED CATEGORIES
CHAPTER 9. CARTESIAN CLOSED CATEGORIES
CHAPTER 10. BICARTESIAN CLOSED CATEGORIES
CHAPTER 11. RESIDUATED CATEGORIES
CHAPTER 12. MONOIDAL BICLOSED CATEGORIES
CHAPTER 13. QUANTIFIER-COMPLETE CATEGORIES
APPENDIX A: THE LABELLED DEDUCTIVE SYSTEM Δ(Χ)
APPENDIX B: THE UNLABELLED DEDUCTIVE SYSTEM Δ(Χ)
APPENDIX C: THE CUT ELIMINATION ALGORITHM
APPENDIX D: THE NORMALIZATION ALGORITHM
BIBLIOGRAPHY
INDEX OF SYMBOLS
INDEX OF SUBJECTS