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Ideas for '', 'Naturalism in Mathematics' and 'Frege's Concept of Numbers as Objects'

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5 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST

18194	'Forcing' can produce new models of ZFC from old models [Maddy]
	Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set.
	From: Penelope Maddy (Naturalism in Mathematics [1997], I.4)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18195	A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
	Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction.
	From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V

18191	Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
	Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals.
	From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII

18193	The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
	Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.
	From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

18169	Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
	Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function.
	From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)