/sci/ - Science & Math » Thread #13996531

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How are STRUCTURES related to FORMAL SYSTEMS?

Anonymous Wed 22 Dec 17:52:56 2021 No.13996531 View Reply Original Report

Quoted By: >>13997548 >>13999041

Genuinely curious.
Not a troll post.
Looking for as much context and detail as possible.
Thanks in advance!

Anonymous

Anonymous Wed 22 Dec 2021 19:04:00 No.13996901 Report

Quoted By: >>13999012

Is there ANY textbook that mentions both of these? I'm not aware if there is, so please inform me.

Anonymous

Anonymous Wed 22 Dec 2021 21:30:33 No.13997548 Report

Quoted By: >>13997576

>>13996531
A formal system is a structure.

Anonymous

Anonymous Wed 22 Dec 2021 21:33:43 No.13997570 Report

Quoted By:

You'd expect any system called "formal" to have a very rigorous definition. But maybe that's just me.

Anonymous

Anonymous Wed 22 Dec 2021 21:35:31 No.13997576 Report

Quoted By:

>>13997548
okay
this is super fucking retarded
you are technically correct that the definition of a structure is a definitional extension, and the formula that defines the new symbol that represents the structure is itself taken as a premise or "axiom" but nobody ever refers to a structure as a formal system in model theory
it's just laughably ridiculous
you'd have the entire class buckling over in tears if you did that
for several minutes
they wouldn't be able to stop laughing

Anonymous

Anonymous Wed 22 Dec 2021 23:41:40 No.13998113 Report

Quoted By:

bumped

Anonymous

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Anonymous Thu 23 Dec 2021 04:11:47 No.13998998 Report

Quoted By:

bumblasted with anime girl butts

Anonymous

Anonymous Thu 23 Dec 2021 04:15:24 No.13999012 Report

Quoted By: >>13999058

>>13996901
any introduction to mathematical logic will mention both of these things
Enderton for example

Anonymous

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Anonymous Thu 23 Dec 2021 04:24:32 No.13999041 Report

Quoted By:

>>13996531
as I understand, it is an interpretation. a model is a structure that satisfies some axioms in a FS I think. I may be wrong i'm just now looking into this.

Anonymous

Anonymous Thu 23 Dec 2021 04:30:58 No.13999058 Report

Quoted By: >>13999070

>>13999012
Wrong. Enderton doesn't mention formal systems, only formal languages.

Anonymous

Anonymous Thu 23 Dec 2021 04:35:25 No.13999070 Report

Quoted By:

>>13999058
Enderton refers to them as "Formal deductions"

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