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set_theory [2015/04/12 17:08] nikolaj |
set_theory [2015/10/08 13:53] nikolaj |
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| ==== Discussion ==== | ==== Discussion ==== | ||
| + | === New symbols === | ||
| + | Most of what follows is concerned with demonstrating existence and uniqueness statements from the axioms and then introducing new symbols ($\emptyset, \omega_{\mathbb N}$, etc.) enabling us to use those propositions more concisely. We understand them as particular terms with particular properties, expressed by the corresponding propositions. | ||
| + | |||
| === Regarding axiom systems and their strengths === | === Regarding axiom systems and their strengths === | ||
| If a logical framework (e.g. first order predicate logic, modus ponens as derivation rule) to work with has been chosen, a collections of axioms for set theory determine how to work with the binary //set membership predicate// "$\in$". | If a logical framework (e.g. first order predicate logic, modus ponens as derivation rule) to work with has been chosen, a collections of axioms for set theory determine how to work with the binary //set membership predicate// "$\in$". | ||
