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Strong Logics of First and Second Order
Strong Logics of First and Second Order

Frege and Hilbert on Consistency
Frege and Hilbert on Consistency

A survey on Interactive Theorem Proving
A survey on Interactive Theorem Proving

... provide communication with other users and systems; the essential point, however, is that this new medium is active, whereas paper, for instance, is not. A.Asperti ...
Hilbert`s Program Then and Now - Philsci
Hilbert`s Program Then and Now - Philsci

... (see Ch. 11) show that the program as originally envisaged by Hilbert cannot be carried out. Although Hilbert’s own project for the foundation of mathematics was ultimately unsuccessful, the project itself and technical advances made in its pursuit have had an enormous impact on logic and the found ...
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PDF

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Programming with Classical Proofs

Structural Logical Relations
Structural Logical Relations

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PPT - UBC Department of CPSC Undergraduates

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Formal systems of fuzzy logic and their fragments∗

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PPT - UBC Department of CPSC Undergraduates

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PPT

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Sketch-as-proof - Norbert Preining

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Computability and Incompleteness

In order to define the notion of proof rigorously, we would have to
In order to define the notion of proof rigorously, we would have to

Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn
Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn

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REVERSE MATHEMATICS, WELL-QUASI

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Reading 2 - UConn Logic Group

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The Z/EVES 2.0 User`s Guide - Department of Computer Science

brouwer`s intuitionism as a self-interpreted mathematical theory
brouwer`s intuitionism as a self-interpreted mathematical theory

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THE LOGIC OF QUANTIFIED STATEMENTS

Henkin`s Method and the Completeness Theorem
Henkin`s Method and the Completeness Theorem

... theory T (pick your favorite one!) is sound and complete in the sense that everything that we can derive from T is true in all models of T , and everything that is true in all models of T is in fact derivable from T . This is a very strong result indeed. One possible reading of it is that the first- ...
Section 1: Propositional Logic
Section 1: Propositional Logic

HONEST ELEMENTARY DEGREES AND DEGREES OF RELATIVE
HONEST ELEMENTARY DEGREES AND DEGREES OF RELATIVE

Cichon`s diagram, regularity properties and ∆ sets of reals.
Cichon`s diagram, regularity properties and ∆ sets of reals.

The Development of Mathematical Logic from Russell to Tarski
The Development of Mathematical Logic from Russell to Tarski

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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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