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Results tagged with foundations
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user 2672
Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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Concrete models of abstract structures
I tried to digest Joel's and Mike's answers and came up with the following picture:
Starting with a model of pure and well-founded set theory we can see it as a class of dots with $\in$-arrows betwe …
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5
answers
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Concrete models of abstract structures
Most mathematicians seem to be contented with the fact, that abstract structures cannot be directly modelled as such in a set theory without ur-elements. What seems to me the standard stance: Set theo …
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2
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Intension vs. Extension: Coextensive relations in model and set theory
(originally posted at MSE as Same same but different: Coextensive relations in model and set theory, slightly modified)
The official definition of a structure in model theory in its presumably most c …
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5
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3
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478
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Counting without one-to-one correspondence? [closed]
Ash and Gross in their wonderful book Fearless Symmetry found it worth mentioning (and thus suggesting) another way of counting for which "we do not even need to know how to count" (in the sense of be …
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2
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Ways to define "definability"
The notion of a definable set is not expressible in the language of set theory: there is no formula $\delta(x)$ that is equivalent with there being a formula $\phi(y)$ such that $x = \lbrace y : \phi( …
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