On reflection principles

On reflection principles

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a serie...

Global Reflection Principles

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.1 To say that the un...

Reflection principles for the continuum∗

Let HC ′ denote the set of sets of hereditary cardinality less than 2ω. We consider reflection principles for HC ′ in analogy with the Levy reflection principle for HC. Let B be a class of complete Boolean algebras. The principle Max(B) says: If R(x1, . . . , xn) is a property which is provably persistent in extensions by elements of B, then R(a1, . . . , an) holds whenever a1, . . . , an ∈ HC ...

Reflection principles in computational logic

Dell'Acqua, P. 1998: Re ection Principles in Computational Logic, Uppsala Theses in Computing Science 30. 154pp. Uppsala. ISSN 0283-359X, ISBN 91-5061298-0. We introduce the concept of re ection principles as a knowledge representation paradigm in a computational logic setting. Re ection principles are expressed as certain kinds of logic schemata intended to capture the basic properties of the ...

Neutron Reflection: Principles and Examples of Applications