Mathematical logic

theorem

consistent theory where every statement is provable or disprovable

theorem

Branch of mathematical logic

thumb|An observer may be able to instantly judge how many red circles are present without counting them, but would find it harder to do so for the greater number of blue circles. Subitizing is the rapid, accurate, and effortless ability to perceive small quantities of items in a set, typically when there are four or fewer items, without relying on linguistic or arithmetic processes. The term refers to the sensation of instantly knowing how many objects are in the visual scene when their number falls within the subitizing range.

combinatorial sequence of numbers

Statement in mathematical logic

statement that can be expressed in the form of a conditional statement with a false antecedent

specific, usually well-known application of a mathematical rule or law

In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions.

term in model theory and related areas of mathematics

interpretation of intuitionistic logic

area of research

in the philosophy of language, a theory of truth holding that truth is a property of sentences

n-ary relation on the domain of a structure whose elements satisfy some formula in the

mathematical symbol

mathematical symbol

model of (first-order) Peano arithmetic that contains non-standard numbers

theorem

simple logical interpretation

Theorem in mathematical logic

1969 non-fiction book by G. Spencer-Brown

The T-schema ("truth schema", not to be confused with "Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it as the "Equivalence Schema", a synonym introduced by Michael Dummett.

in mathematical logic, property of formula that has the same truth value in each of some class of structures

logical expression whose terms do not contain any variables

formal operation that transforms a predicate into a relation

subject field of Boolean algebra discussing changes of Boolean variables and functions

subset of a structure that itself forms a structure

structure over a vocabulary defined solely by syntactical properties

result demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general

given a model of a theory over a 1st-order language, the set of atomic sententences and negations thereof of that hold in the model, when the language is extended with constant symbols for each element in the domain in the model

viewpoint in the philosophy of mathematics

method in mathematical logic