Re: Continuum hypothesis

On Aug 17, 4:00 pm, george <gree...@xxxxxxxxxx> wrote:
Don't panic: simpler than you think. It is NOT a higher more
complicated kind
of number theory. It just means number theory USING FIRST-ORDER
LOGIC,
using syntax and semantics that are about numbers and sets (or
predicates) of
numbers, BUT NOT about Sets OF SETS of numbers (THAT would be *2nd*-
order arithmetic).

Hang on, wouldn't quantifying over sets of numbers put you in 2nd
order arithmetic?


.

Relevant Pages

  • Re: man page syntax for +script
    ... The man pages for [bind] and [comm hook] both describe how you can either replace the current script or append to it, but they give slightly different syntaxes. ... But the syntax for makes it appear that the + and the script are separate arguments, and that caused me some confusion. ... you have a distorted view of what is syntax and what is semantics in Tcl. ...
    (comp.lang.tcl)
  • Re: man page syntax for +script
    ... The man pages for and both describe how you can either replace the current script or append to it, but they give slightly different syntaxes. ... But the syntax for makes it appear that the + and the script are separate arguments, and that caused me some confusion. ... The plus is a semantic definition that these two unrelated commands put on their last argument, expr has a very different semantic definition of "+". ... you have a distorted view of what is syntax and what is semantics in Tcl. ...
    (comp.lang.tcl)
  • Re: Formalisation
    ... first-order theories FOUNDED ON RECURSIVE AXIOM-SETS. ... ZFC then THAT, AGAIN, is a recursively axiomatizable theory ... invites SEMANTICS IN TOTO to be COMPLETELY EXILED ...
    (sci.logic)
  • Re: 2nd-order logic in lower-order language
    ... subclasses of the class of all individuals. ... The first-order quantifiers are already ... We are going to stick with the class of unary predicates over the ...
    (sci.logic)
  • Re: MV Keys
    ... In *practise*, you may not need to worry ... Through creative use of syntax, ... I don't envision a separate language; ... even within the given semantics. ...
    (comp.databases.theory)