Cumulus
发表于 2025-3-28 15:26:47
Classes, i.e., given a wff . (.) containing no free variables other than x, there exists a set that contains all objects for which . (.) holds and contains no object for which .(.) does not hold. More formally ..
自由职业者
发表于 2025-3-28 20:22:33
Ordinal Numbers,925) and Bertrand Russell (1872–1970), working independently, who removed Cantor’s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism.
GIBE
发表于 2025-3-29 00:49:37
http://reply.papertrans.cn/48/4735/473452/473452_43.png
landfill
发表于 2025-3-29 03:41:46
http://reply.papertrans.cn/48/4735/473452/473452_44.png
Biomarker
发表于 2025-3-29 09:25:13
The Arithmetization of Model Theory, a set, that is, “m is a standard model of ZF” can be expressed as a single sentence in ZF. The basic objective of this section is to produce such a sentence. Our approach is to assign Gödel numbers to the well formed formulas of our language. This assignment will be made by the mapping . of Definition 15.2.
Monotonous
发表于 2025-3-29 12:10:46
http://reply.papertrans.cn/48/4735/473452/473452_46.png
水槽
发表于 2025-3-29 16:10:30
http://reply.papertrans.cn/48/4735/473452/473452_47.png
愤世嫉俗者
发表于 2025-3-29 21:40:37
Equality,uivalent under alphabetic change of variable, we intend . to be an abbreviation for. This problem is easily resolved by specifying that . is the first variable an our list . that is distinct from . and from .. Having thereby shown that we can specify a particular formula we will not bother to do so
Affection
发表于 2025-3-30 00:38:28
http://reply.papertrans.cn/48/4735/473452/473452_49.png
阴险
发表于 2025-3-30 06:26:19
http://reply.papertrans.cn/48/4735/473452/473452_50.png