What is Mathematics: Gödel's Theorem and Around
by Karlis Podnieks
Publisher: University of Latvia 2013
Number of pages: 239
Hyper-textbook for students in mathematical logic and foundations of mathematics. Contents: Platonism, intuition and the nature of mathematics; Axiomatic Set Theory; First Order Arithmetic; Hilbert's Tenth Problem; Incompleteness Theorems; Around Goedel's Theorem.
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by Vilnis Detlovs, Karlis Podnieks - University of Latvia
From the table of contents: 1. Introduction. What Is Logic, Really?; 2. Propositional Logic; 3. Predicate Logic; 4. Completeness Theorems (Model Theory); 5. Normal Forms. Resolution Method; 6. Miscellaneous (Negation as Contradiction or Absurdity).
by Wolfgang Rautenberg - Springer
A well-written introduction to the beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Goedel's incompleteness theorems, as well as some topics motivated by applications.
by Frank Waaldijk - arXiv
We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism.
by Nuel Belnap - University of Pittsburgh
Contents: Grammar; The art of the logic of truth-functional connectives; Quantifier proofs; A modicum of set theory; Symbolizing English quantifiers; Quantifier semantics - interpretation and counterexample; Theories; Definitions.