# Veblen Hierarchy

Formalized Mathematics (2011)

- Volume: 19, Issue: 2, page 83-92
- ISSN: 1426-2630

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topGrzegorz Bancerek. "Veblen Hierarchy." Formalized Mathematics 19.2 (2011): 83-92. <http://eudml.org/doc/267399>.

@article{GrzegorzBancerek2011,

abstract = {The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ.The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets). It is done with use of universal sets (Tarski classes). Namely, we define the Veblen functions in a given universal set and φα(β) as a value of Veblen function from the smallest universal set including α and β.},

author = {Grzegorz Bancerek},

journal = {Formalized Mathematics},

keywords = {Mizar; Veblen hierarchy; Veblen functions},

language = {eng},

number = {2},

pages = {83-92},

title = {Veblen Hierarchy},

url = {http://eudml.org/doc/267399},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Grzegorz Bancerek

TI - Veblen Hierarchy

JO - Formalized Mathematics

PY - 2011

VL - 19

IS - 2

SP - 83

EP - 92

AB - The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ.The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets). It is done with use of universal sets (Tarski classes). Namely, we define the Veblen functions in a given universal set and φα(β) as a value of Veblen function from the smallest universal set including α and β.

LA - eng

KW - Mizar; Veblen hierarchy; Veblen functions

UR - http://eudml.org/doc/267399

ER -

## References

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