Title: Theory / Unimportant / Math / Al gebra / Universal / Burris-Sankappanavar+16{
Tags: hasSeenConjDef

Question: ￼Is \(N_5\) distributive ?
Answer: No
Page: 13
Chapter: I
Section: 3

Question: ￼Is \(N_5\) modular ?
Answer: No
Page: 13
Chapter: I
Section: 3

Definition: The subalgebra of \(\mathbf B\) with universe \(\alpha(A)\)
Page: 32
Chapter: II
Section: 2
Variables: \(\mathcal F\) a type
\(\mathbf{A,B}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
\(\alpha:\mathbf{A\to B}\)
Notation: \(\alpha(\mathbf A)\)

Name: Structure theorems
Definition: every member of \(K\) isomorphic to some member of \(K_1\)
Page: 32
Chapter: II
Section: 2
Variables: \(K\) a class of algebra
Definition2: every member of \(K\) is embeddable in some member of \(K_1\)
Conjdef: finding some \(K_1\subseteq K\) such that, either

Name: The subuniverse generated by \(X\)
Definition: \(\bigcap \{B\supseteq X\mid B\text{ is a subuniverse of }\mathbf A\}\)
Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
\(X\subseteq A\)
Index: 1
Kind: Def
Abbreviation: \(\mathbf{Sg}(X)\)
Typ: subuniverse of \(\mathbf A\)

Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
\(X\subseteq A\)
Notation: \(\mathbf{Sg}\)
Index: 1
Kind: Def
Property: Closure operator

Definition: The set of subuniverses of \(\mathbf A\)
Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
Notation: \(\mathrm{Sub}(\mathbf A)\)
Kind: Cor
Typ: Algebraic lattice for \(\subseteq\)

Definition: The subuniverses of \(\mathbf A\)
Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
Notation: \(\mathbf{Sub}(\mathbf A)\)
Kind: Cor
Typ: lattice

Name: A set which generates \(\mathbf A\)
Definition: A set \(X\subseteq A\) such that \(\mathrm{Sg}(X)=A\)
Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
Kind: Cor
Name2: A set of generator of \(\mathbf A\)

Name: A finitely generated algebra \(\mathbf A\)
Definition: An algebra which has a finite set of generator
Page: 33
Chapter: II
Section: 3
Variables: \(\mathcal F\) a type
\(\mathbf{A}=\langle A,\mathcal F\rangle\) algebras of type \(\mathcal F\),
Kind: Cor