Re: Scott and George's Teaching Thread

On Aug 23, 2:43 pm, george <gree...@xxxxxxxxxx> wrote:
No, we don't. Definitions ARE NOT axioms, although some axioms
should be thought of as definitions. It ABSOLUTELY WILL HELP
your understanding HERE, at the BEGINNING, to treat Def/Thm/Ax as
a trichotomy. "Is this a Def, a Thm, or an Ax?" is a question that
will
SPARE you confusion! ASK IT FREQUENTLY!
Subset as presented here is a Def AND NOT an Ax.

Okay, so e is the only predicate in set theory.

A definition is like a macro, its just a syntactical re-arrangement of
symbols whose overall meaning does not change. So are &, |, ~, ->, and
<-> macros for predicates of FOL; ie, & is a macro for AND(t1,t2),
etc.?

The notation "U c V =df Ax[xeU -> xeV]" is a notation used strictly
for readability, which means everywhere I see "UcV" I should replace
with "Ax[xeU -> xeV]"; eg, UcVcW is equivalent to Ax[xeU -> xeV ->
xeW]. Correct?

.

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