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 Notes on 【Logc for mathematicians】A.G.Hamilton
10-15-2017, 11:59 AM (This post was last modified: 10-15-2017 12:50 PM by elim.)
Post: #1
 elim Moderator     Posts: 581 Joined: Feb 2010 Reputation: 0
Notes on 【Logc for mathematicians】A.G.Hamilton
Don't see a clair text in basic concepts of Mathematical Logic. This one is not pretend to be at the begining. This saved some complecities that otherwise didn't doing better....

Simiple statement .....

Compound statement Finite composition of finite number
of simple statements and connectives $\lnot,\;\wedge,\,\vee,\,\to,\,\leftrightarrow.$
In other words, we call statements of the form
$\qquad A,\,\lnot A,\, A\wedge B,\,A\vee B,\,A\to B,\, A\leftrightarrow B\qquad(\dagger)$
compound statements where $A,\,B$ are simple statements.
Now inductively statements of the form $\,(\dagger)\,$are called
compound statements if$\,A,\,B\,$are compound statements.
10-16-2017, 04:29 PM (This post was last modified: 10-16-2017 04:38 PM by elim.)
Post: #2
 elim Moderator     Posts: 581 Joined: Feb 2010 Reputation: 0
Statement Variable
I always wondering what a veriable mean, or how it be defined in set theory term.

I guess is a veriable is a pair $(v,\mathbb{id}_D)$ where $\mathbb{id}_D: u\mapsto u$ is the identity mapping on a set $D$ while $v$ is a lable or a name of the mapping. Usually, for short we use $v$ instead of $(v,\mathbb{id}_D)$
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