intuitionistic type theory - Article Index

Encyclopedia - Type: Encyclopedia - Type
Type has historically had the following uses: In biology, a type is the specimen or specimens upon which an original species description...   » Read the article

Encyclopedia - Anders Martin-löf: Encyclopedia - Anders Martin-löf
Anders Martin-Löf is a Swedish mathematician. He is the brother of Per Martin-Löf. (Who was responsible for a pioneering definition of ...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia - Axiom Of Choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo. While it was originall...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Usage
Until the late 19th century, the axiom of choice was often used implicitly. For example, after having established that the set X contains...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - History
Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Peano, Russell and Dedekind, conventi...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Results Requiring Choice In Intuitionistic Logic, Though Not Classically
Interestingly, in various varieties of constructive logic (in particular, intuitionistic logic) in which the law of excluded middle is no...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Tableau Systems
Main article: Tableau systems Tableau systems apply the central idea of analytic proof from structural proof theory to provide decision p...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Structural Proof Theory
Main article: Structural proof theory Structural proof theory is the subdiscipline of proof theory that studies proof calculi that suppor...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Ordinal Analysis
Main article: Ordinal analysis Ordinal analysis is a powerful technique for providing combinatorial consistency proofs for theories forma...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Consistency Proofs
Main article: Consistency proof As we have discussed, the spur for the mathematical investigation of proofs in formal theories was Hilber...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Results Requiring ¬ac
There are models of Zermelo-Fraenkel set theory in which the axiom of choice is false. We will abbreviate "Zermelo-Fraenkel set theory pl...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Statement
The axiom of choice states: Let X be a set of non-empty sets. Then we can choose a member from each set in X. Stated more formally: Let X...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Independence Of Ac
By work of Kurt Gödel and Paul Cohen, the axiom of choice is logically independent of the other axioms of Zermelo-Fraenkel set theory (Z...   » Read the article

Encyclopedia - Axiom Of Choice: Encyclopedia Ii - Axiom Of Choice - Results Requiring Choice In Intuitionistic Logic Though Not Classically
Interestingly, in various varieties of constructive logic (in particular, intuitionistic logic) in which the law of excluded middle is no...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Formal And Informal Proof
However, the proofs used in everyday mathematical practice are almost never like the formal proofs in proof theory. They are rather like ...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Kinds Of Proof Calculus
The three most well known proof calculi are: The Hilbert-style calculi The natural deduction calculus The sequent calculus To say these...   » Read the article