Mathematical Symbols

[mikeyp]

The symbol |- is used to mean 'implies'

What does the symbol |= mean?

[THECORBYLOON]

mikeyp I've seen => (there should be no gap but I can't get the proper symbol) used to mean implies but not I-, what country are you in?

[QmunkE]

Indeed, the implication symbols I know look like

=>

Perhaps the other one you have is meant to be:

<==> which is equivalence or "if and only if" ?

[magicdice]

QmunkE i thought <==> meant that they were mutually implicit?

[QmunkE]

Apologies, the <==> is the "is-equivalent-to" connective, but is not the same as "logical equivalence" unless p <==> q is a tautology.

(p => q) ^ (q => p) = (p <=> q)

[mikeyp]

Thanks for your effort guys. Yeah => can mean implies too. Basically, I can't figure out what the symbol means. I think i've managed to do what I need to despite it. I'm revising for an exam, and this came up on one of the lecture slides. I reckon I can answer around it, should be fine!

[magicdice]

sorry we couldn't be any more help. good luck with your exam!

[Peter Pedant]

Sorry mikey I am a bit late on this.

The first one is a turnstyle, first used by Frege i think, and means implies when used with axioms.

the second sign is a double turnstyle and means = logically valid or equivalent

Both terms are in Boolos and Jeffrey, Intro to computability and logic 3rd edition

you cannot imagine my shock at seeing this question - considering what I usually see, it was totally unexpected

[Peter Pedant]

We're in the country called first order logic, Corby

Sorry MIke the double turnstyle means 'satisfies'. I will use ~ - no no I've seen how to do I=

U satisfies w with assignment s is written U I= w(s)

 I= is not a part of a first order language but is used to describe things about the language, and so is said to be metalanguage. Yup that's it

You havent just picked up the book have you? you should start at page 1. Boolos and J is a bit of a hard read, howver the OU do an excellent course on it MST 384 I think - Number Theory and Computability and Logic

[Peter Pedant]

How did the exam go, and did it come up?