Logic, sets

[charlie]

Let f : X → X be a function. For A ⊆ X defineC∗(A) = /\{B ⊆ X : A ⊆ B and f(B) ⊆ B}
Define a subset C∗(A) of X as follows. Defineby recursion subsets C0, C1, C2, . . . of X byC0 = ACn+1 = Cn ∪ f(Cn) for every n ≥ 0.
C∗(A) = ∪_n∈ωCn
(a) Prove that f(C∗(A)) ⊆ C∗(A) and that C∗(A) is the smallest subset of X with thisproperty which contains A (namely C∗(A) is contained in any B ⊆ X such that A ⊆ Band f(B) ⊆ B).
(b) Prove that f(C∗(A)) ⊆ C∗(A) and deduce that C∗(A) ⊆ C∗(A).
(c) Prove that if B ⊆ X has the property that A ⊆ B and f(B) ⊆ B then Cn ⊆ B forevery n ∈ ω. Deduce that C∗(A) ⊆ B and that C∗(A) = C∗(A).

 

[stapel]

Let f : X → X be a function. For A ⊆ X defineC∗(A) = /\{B ⊆ X : A ⊆ B and f(B) ⊆ B}

What is the meaning of the "/\" notation? (I've seen something similar being used to indicate a logical "and", but I'm not familiar with whatever you're using.)

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!