Title: Theory / Unimportant / Math / Al gebra / Universal / Burris-Sankappanavar+16{ / Part2
Tags: récupéré closed fromMath

Smaller0: \(a\land b=0\) and \(a\lor b=1\)
Greater0: \(a=b'\)
Page: 130
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
Index: 2
Smaller to greater: iff
Context: Boolean algebras

Smaller0: \((a\lor b)'\)
Greater0: \(a'\land b'\)
Page: 130
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
Index: 2
Smaller to greater: \(\equiv\)

Smaller0: \((a\land b)'\)
Greater0: \(a'\lor b'\)
Page: 130
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
Index: 2
Smaller to greater: \(\equiv\)

Name: The Boolean algebr of subsets of \(X\)
Definition: The Boolean algebra \(\langle\mathrm{Su}(X),\cup,\cap,Y\mapsto X\setminus Y, \emptyset,X\rangle\)
Page: 131
Chapter: IV
Section: 1
Variables: \(X\) a set
Notation: \(\mathbf{Su}(X)\)
Index: 3
Kind: Def
Definition2: \(\mathbf{2}^X\)

Name: The set of subsets of \(X\)
Page: 131
Chapter: IV
Section: 1
Variables: \(X\) a set
Notation: \(\mathrm{Su}(X)\)
Index: 3
Kind: Def

Definition: \(\mathbf{Su}(\{x\})\)
Page: 131
Chapter: IV
Section: 1
Context: Boolean algebras
Notation: \(\mathbf 2\)
Index: 3
Kind: Def

Definition: \(\mathbf{Su}(\{\})\)
Page: 131
Chapter: IV
Section: 1
Context: Boolean algebras
Notation: \(\mathbf 1\)
Index: 3
Kind: Def

Definition: the set of \(x\in X\) such that \(a\le x\)
Page: 132
Chapter: IV
Section: 1
Variables: \((X,\le)\) an ordered set,
\(a\le b\in X\)
Notation: \([a,b]\)
Index: 3
Kind: Def

Definition: The subalgebra with universe \([0,a]\)
Page: 132
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
\(a\in B\)
Notation: \(\mathbf B\upharpoonright a\)
Index: 3
Kind: Def

Name: Boolean alegbras
Page: 132
Section: 1
Chapter: IV
Index: 4
Kind: Lem
Under: \(\upharpoonright a\) for \(a\) an element of the BA

Definition: [$]\defFun{B}{B\upharpoonright a}{b}{a\land b}[/$]
Page: 132
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
\(a\in B\)
Notation: \(\alpha_a\)
Index: 7
Kind: Lem
Typ: Surjective homomophism

Question: \(\mathbf B\upharpoonright a\times\mathbf B\upharpoonright a'\)
Answer: is isomorphic to \(\mathbf B\)
Page: 132
Chapter: IV
Section: 1
Variables: \(\mathbf B\) a Boolean algebra
\(a\in B\)
Index: 4
Kind: Lem
Construction: \(b\mapsto(\alpha_a(b),\alpha_{a'}(b))\)