Expansions of real closed fields that introduce no new smooth functions
We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Eleftheriou, Pantelis E. [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Traditional knowledge and the BBNJ instrument - Mulalap, Clement Yow ELSEVIER, 2020, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:171 ; year:2020 ; number:7 ; pages:0 |
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| DOI / URN: |
10.1016/j.apal.2020.102808 |
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| 520 | |a We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semialgebraic. | ||
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10.1016/j.apal.2020.102808 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001009.pica (DE-627)ELV050279556 (ELSEVIER)S0168-0072(20)30032-4 DE-627 ger DE-627 rakwb eng 550 VZ INTRECHT DE-1a fid 83.00 bkl Eleftheriou, Pantelis E. verfasserin aut Expansions of real closed fields that introduce no new smooth functions 2020 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semialgebraic. secondary Elsevier 14P20 Elsevier 03C45 Elsevier primary Elsevier Savatovsky, Alex oth Enthalten in Elsevier Mulalap, Clement Yow ELSEVIER Traditional knowledge and the BBNJ instrument 2020 Amsterdam [u.a.] (DE-627)ELV005164354 volume:171 year:2020 number:7 pages:0 https://doi.org/10.1016/j.apal.2020.102808 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-INTRECHT 83.00 Volkswirtschaft: Allgemeines VZ AR 171 2020 7 0 |
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We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semialgebraic. |
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We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semialgebraic. |
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We prove the following theorem: let R ˜ be an expansion of the real field R ‾ , such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f : X ⊆ R n → R with open semialgebraic domain is semialgebraic. |
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