Theories in maths which do not use the axiom of choice.

MathematicalPhysicist
Science Advisor
Gold Member
Messages
4,662
Reaction score
372
i read that there are some logicians who do not use the axiom of choice in their axioms systems. i wonder what is the math that isn't using the axiom of choice, or what theories do not use it?
 
Physics news on Phys.org
A lot of theories do not use the axiom of choice. Pretty much any discrete mathematics (i.e. with finite sets only) won't use it. Most of real analysis has no need to invoke the axiom of choice. Most algebra gets by without needing the axiom of choice to be invoked. You don't really ever need an algebraic closure of anything, for instance: start with a ground field, decide what polys you need to have roots, this will normally only be a finite number, and add in the roots accordingly. The vast majority of algebra only ever deals in finite dimensional vector spaces.

Incidentally, it is not just logicians who chose to use or ignore the axiom of choice specifically. Completely unjustified statistic alert: you can probably get by doing 99% of maths without ever needing to invoke the axiom of choice.
 
i should have been clearer, i meant theories of sets which do not use AC.
 

Thread 'Here's a Statistics problem for game of Polo (or Hockey if you like)'

Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
View full post »

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »

Similar threads

I Axiom of Choice: Choosing Identical Objects
Replies
7
Views
2K
A About the “Axiom of Dependent Choice”
Replies
2
Views
2K
MHB About the “Axiom of Dependent Choice”
Replies
1
Views
2K
A First order logic and set theory: who comes first?
Replies
2
Views
3K
MHB Axioms of Set Theory .... and the Union of Two Sets ....
Replies
2
Views
2K
A Concrete examples of randomness in math vs. probability theory
Replies
11
Views
2K
A Axiom of choice: Replacing a strong condition with a weaker condition
Replies
6
Views
3K
MHB ZFC .... Axioms of Foundation .... and Infinity ....
Replies
9
Views
3K
What Makes the Axiom of Choice So Controversial?
Replies
49
Views
5K
MHB ZFC and the Axiom of Power Sets ....
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top