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a-logic - Digital Commons@Wayne State University
a-logic - Digital [email protected] State University

Revising the AGM Postulates
Revising the AGM Postulates

code-carrying theory - Computer Science at RPI
code-carrying theory - Computer Science at RPI

a thesis submitted in partial fulfillment of the requirements for the
a thesis submitted in partial fulfillment of the requirements for the

Principia Logico-Metaphysica (Draft/Excerpt)
Principia Logico-Metaphysica (Draft/Excerpt)

X - NUS School of Computing
X - NUS School of Computing

X - NUS School of Computing
X - NUS School of Computing

Ribbon Proofs - A Proof System for the Logic of Bunched Implications
Ribbon Proofs - A Proof System for the Logic of Bunched Implications

Discrete Mathematics
Discrete Mathematics

Some Aspects and Examples of Innity Notions T ZF
Some Aspects and Examples of In nity Notions T ZF

Interpretability formalized
Interpretability formalized

Incompleteness
Incompleteness

relevance logic - Consequently.org
relevance logic - Consequently.org

Bridge to Abstract Mathematics: Mathematical Proof and
Bridge to Abstract Mathematics: Mathematical Proof and

Higher Order Logic - Theory and Logic Group
Higher Order Logic - Theory and Logic Group

... From the second order characterization of Ns there follows a second order interpretation of the true formulas of Peano's Arithmetic, PA. Let 7 Theorem 2.3.1 shows that a particular countable structure, that of the natural numbers, is characterized up to isomorphism by its second order theory. A natu ...
Higher Order Logic - Indiana University
Higher Order Logic - Indiana University

A BOUND FOR DICKSON`S LEMMA 1. Introduction Consider the
A BOUND FOR DICKSON`S LEMMA 1. Introduction Consider the

Lectures on Sieve Methods - School of Mathematics, TIFR
Lectures on Sieve Methods - School of Mathematics, TIFR

Formale Methoden der Softwaretechnik Formal methods of software
Formale Methoden der Softwaretechnik Formal methods of software

Logic Part II: Intuitionistic Logic and Natural Deduction
Logic Part II: Intuitionistic Logic and Natural Deduction

Notes on the ACL2 Logic
Notes on the ACL2 Logic

... important in the ACL2 logic! More below. This example highlights the new tool we have that will allow us to reason about programs: proof. The game we will be playing is to construct proofs of conjectures involving some of the basic functions we have already defined (e.g., len, app, rev). We will foc ...
Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011
Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011

Per Lindström FIRST
Per Lindström FIRST

Abella: A System for Reasoning about Relational Specifications
Abella: A System for Reasoning about Relational Specifications

Functional Dependencies in a Relational Database and
Functional Dependencies in a Relational Database and

1 2 3 4 5 ... 27 >

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.
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