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See all on Wikipediahttps://en.wikipedia.org/wiki/Mathematical_logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive … See more
The Handbook of Mathematical Logic in 1977 makes a rough division of contemporary mathematical logic into four areas:
1. set theory
2. model theory See moreSet theory is the study of sets, which are abstract collections of objects. Many of the basic notions, such as ordinal and cardinal numbers, were developed informally by Cantor before formal axiomatizations of set theory were developed. The first such axiomatization, … See more
Recursion theory, also called computability theory, studies the properties of computable functions and the Turing degrees, which divide the uncomputable functions into sets that have the same level of uncomputability. Recursion theory also includes the … See more
Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics. … See more
At its core, mathematical logic deals with mathematical concepts expressed using formal logical systems. These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language. The systems of See more
Model theory studies the models of various formal theories. Here a theory is a set of formulas in a particular formal logic and signature, while a model is a structure that gives a concrete interpretation of the theory. Model theory is closely related to universal algebra See more
Proof theory is the study of formal proofs in various logical deduction systems. These proofs are represented as formal mathematical objects, facilitating their analysis by … See more
Wikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Wikipedia:Contents/Mathematics_and_logic
WebWikipedia's contents: Mathematics and logic edit · watch Mathematics is the study of topics such as quantity (numbers), structure, space, and change. It evolved through the …
- https://simple.wikipedia.org/wiki/Mathematical_logic
WebMathematical logic is a field of mathematics that tries to formalize logic so that it can be used for mathematics more easily. Logic is about reasoning, and mathematical logic …
- https://en.wikipedia.org/wiki/Category:Mathematical_logic
WebMathematical logic has several meanings in common usage. It originally referred to symbolic or formal logic, and then came to be associated with the study of the logical …
- https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula , the symbol is a predicate that applies to the individual constant . Similarly, in the formula , the symbol is a predicate that applies to the individual constants and .
In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula would be true on an interpretation if the entities denote…Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 2 mins
- https://en.wikipedia.org/wiki/Structure_(mathematical_logic)
WebThe domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), its universe (especially in model …
- https://en.wikipedia.org/wiki/Logic
WebMathematical theories were supposed to be logical tautologies, and the programme was to show this by means of a reduction of mathematics to logic. The various attempts to carry this out met with failure, from the …
- https://en.wikipedia.org/wiki/Mathematics
WebThe two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic, although used for …
- https://math.stackexchange.com/questions/1993596
WebNov 1, 2016 · Mathematical logic means many things, depending on context. In particular, it includes two related areas of study: Using mathematical to study "logical" topics such …
- https://simple.wikipedia.org/wiki/Mathematics
WebMost mathematicians use non-logical and creative reasoning in order to find a logical proof. Sometimes, mathematics finds and studies rules or ideas that we don't understand yet. …
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