An Example of Induction: Fibonacci Numbers
An Example of Induction: Fibonacci Numbers

... This short document is an example of an induction proof. Our goal is to rigorously prove something we observed experimentally in class, that every fifth Fibonacci number is a multiple of 5. As usual in mathematics, we have to start by carefully defining the objects we are studying. Definition. The s ...
Lecture Notes
Lecture Notes

possible-worlds semantics for modal notions conceived as predicates
possible-worlds semantics for modal notions conceived as predicates

Document
Document

Identity in modal logic theorem proving
Identity in modal logic theorem proving

PDF
PDF

Mathematical Induction
Mathematical Induction

Lecture 06
Lecture 06

Complete Sequent Calculi for Induction and Infinite Descent
Complete Sequent Calculi for Induction and Infinite Descent

CS243: Discrete Structures Mathematical Proof Techniques
CS243: Discrete Structures Mathematical Proof Techniques

Section 3 - The Open University
Section 3 - The Open University

On Herbrand`s Theorem - UCSD Mathematics
On Herbrand`s Theorem - UCSD Mathematics

Soundness and Completeness - Cognitive Science Department
Soundness and Completeness - Cognitive Science Department

... One can see graphs with multiple cuts inside each other as expressing recursively conditioned conditionals. For example: ...
Handout for - Wilfrid Hodges
Handout for - Wilfrid Hodges

Mathematical Logic. An Introduction
Mathematical Logic. An Introduction

(pdf)
(pdf)

CSE 20 - Lecture 14: Logic and Proof Techniques
CSE 20 - Lecture 14: Logic and Proof Techniques

YABLO WITHOUT GODEL
YABLO WITHOUT GODEL

Basic Logic and Fregean Set Theory - MSCS
Basic Logic and Fregean Set Theory - MSCS

Proofs by Contradiction and Contraposition
Proofs by Contradiction and Contraposition

On Action Logic
On Action Logic

Notes on Classical Propositional Logic
Notes on Classical Propositional Logic

Beal`s conjecture - from Jim H. Adams on
Beal`s conjecture - from Jim H. Adams on

Contents MATH/MTHE 217 Algebraic Structures with Applications Lecture Notes
Contents MATH/MTHE 217 Algebraic Structures with Applications Lecture Notes

Lecture 1: Elements of Mathematical Logic
Lecture 1: Elements of Mathematical Logic

Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an ""effective procedure"" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.