Автор статьи
Валерия
Эксперт по сдаче вступительных испытаний в ВУЗах
- Atomic BAs, already mentioned above.
- Atomless BAs, which are defined to be BAs without any atoms. For example, any infinite free BA is atomless.
- Complete BAs, defined above. These are especially important in the foundations of set theory.
- Interval algebras. These are derived from linearly ordered sets (L, <) with a first element as follows. One takes the smallest algebra of subsets of L containing all of the half-open intervals [a, b) with a in L and b in L or equal to ∞. These BAs are useful in the study of Lindenbaum-Tarski algebras. Every countable BA is isomorphic to an interval algebra, and thus a countable BA can be described by indicating an ordered set such that it is isomorphic to the corresponding interval algebra.
- Tree algebras. A tree is a partially ordered set (T, <) in which the set of predecessors of any element is well-ordered. Given such a tree, one considers the algebra of subsets of T generated by all sets of the form {b : a ≤ b} for some a in T.
- Superatomic BAs. These are BAs which are not only atomic, but are such that each subalgebra and homomorphic image is atomic.
- A finite set of symbols which can be used for constructing formulae.
- A grammar, i.e. a way of constructing well-formed formulae out of the symbols, such that it is possible to find a decision procedure for deciding whether a formula is a well-formed formula (wff) or not.
- A set of axioms or axiom schemata: each axiom has to be a wff.
- A set of inference rules.
- A set of theorems. This set includes all the axioms, plus all wffs which can be derived from previously-derived theorems by means of rules of inference. Unlike the grammar for wffs, there is no guarantee that there will be a decision procedure for deciding whether a given wff is a theorem or not.
- What is formalization?
- What are formal proofs?
- What was the role of Davia Hilbert in formal systems?
- What are the components of Mathematical formal system?
О сайте
Ссылка на первоисточник:
http://pgtk.edu.ru
Поделитесь в соцсетях: