Admissible closures of polynomial time computable arithmetic
We propose two admissible closures and of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) is conservative over PTCA with respect to sentences, and (ii) is conservat...
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| Veröffentlicht in: | Archive for mathematical logic 2011-07, Vol.50 (5-6), p.643-660 |
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| container_title | Archive for mathematical logic |
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| creator | Probst, Dieter Strahm, Thomas |
| description | We propose two admissible closures
and
of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i)
is conservative over PTCA with respect to
sentences, and (ii)
is conservative over full bounded arithmetic PHCA for
sentences. This yields that (i) the
definable functions of
are the polytime functions, and (ii) the
definable functions of
are the functions in the polynomial time hierarchy. |
| doi_str_mv | 10.1007/s00153-011-0238-7 |
| format | Article |
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and
of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i)
is conservative over PTCA with respect to
sentences, and (ii)
is conservative over full bounded arithmetic PHCA for
sentences. This yields that (i) the
definable functions of
are the polytime functions, and (ii) the
definable functions of
are the functions in the polynomial time hierarchy.</description><identifier>ISSN: 0933-5846</identifier><identifier>EISSN: 1432-0665</identifier><identifier>DOI: 10.1007/s00153-011-0238-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Algebra ; Archives ; Arithmetic ; Hierarchies ; Mathematical analysis ; Mathematical functions ; Mathematical logic ; Mathematical Logic and Foundations ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Original Article ; Polynomials ; Sentences</subject><ispartof>Archive for mathematical logic, 2011-07, Vol.50 (5-6), p.643-660</ispartof><rights>Springer-Verlag 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c342t-f8b6e4b7722652ac61a82adf0cef2feea85746855c5a9c6332b09ee19a3b16613</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00153-011-0238-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00153-011-0238-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Probst, Dieter</creatorcontrib><creatorcontrib>Strahm, Thomas</creatorcontrib><title>Admissible closures of polynomial time computable arithmetic</title><title>Archive for mathematical logic</title><addtitle>Arch. Math. Logic</addtitle><description>We propose two admissible closures
and
of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i)
is conservative over PTCA with respect to
sentences, and (ii)
is conservative over full bounded arithmetic PHCA for
sentences. This yields that (i) the
definable functions of
are the polytime functions, and (ii) the
definable functions of
are the functions in the polynomial time hierarchy.</description><subject>Algebra</subject><subject>Archives</subject><subject>Arithmetic</subject><subject>Hierarchies</subject><subject>Mathematical analysis</subject><subject>Mathematical functions</subject><subject>Mathematical logic</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Article</subject><subject>Polynomials</subject><subject>Sentences</subject><issn>0933-5846</issn><issn>1432-0665</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhoMouK7-AG_Fi6doPpqPgpdlcVVY8KLnkGYn2qVtatIe9t-bpYIgeJrDPO_LzIPQNSV3lBB1nwihgmNCKSaMa6xO0IKWnGEipThFC1JxjoUu5Tm6SGmfaaY1XaCH1a5rUmrqFgrXhjRFSEXwxRDaQx-6xrbF2HR5F7phGu0Rs7EZPzsYG3eJzrxtE1z9zCV63zy-rZ_x9vXpZb3aYsdLNmKvawllrRRjUjDrJLWa2Z0nDjzzAFYLVUothBO2cpJzVpMKgFaW11RKypfodu4dYviaII0m3-ygbW0PYUpG66okvMwvLtHNH3Ifptjn44yWFa-0kiRDdIZcDClF8GaITWfjwVBijjbNbNNkm-Zo06icYXMmZbb_gPhb_H_oGzJZdwk</recordid><startdate>20110701</startdate><enddate>20110701</enddate><creator>Probst, Dieter</creator><creator>Strahm, Thomas</creator><general>Springer-Verlag</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110701</creationdate><title>Admissible closures of polynomial time computable arithmetic</title><author>Probst, Dieter ; Strahm, Thomas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c342t-f8b6e4b7722652ac61a82adf0cef2feea85746855c5a9c6332b09ee19a3b16613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Algebra</topic><topic>Archives</topic><topic>Arithmetic</topic><topic>Hierarchies</topic><topic>Mathematical analysis</topic><topic>Mathematical functions</topic><topic>Mathematical logic</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Article</topic><topic>Polynomials</topic><topic>Sentences</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Probst, Dieter</creatorcontrib><creatorcontrib>Strahm, Thomas</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Archive for mathematical logic</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Probst, Dieter</au><au>Strahm, Thomas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Admissible closures of polynomial time computable arithmetic</atitle><jtitle>Archive for mathematical logic</jtitle><stitle>Arch. Math. Logic</stitle><date>2011-07-01</date><risdate>2011</risdate><volume>50</volume><issue>5-6</issue><spage>643</spage><epage>660</epage><pages>643-660</pages><issn>0933-5846</issn><eissn>1432-0665</eissn><abstract>We propose two admissible closures
and
of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i)
is conservative over PTCA with respect to
sentences, and (ii)
is conservative over full bounded arithmetic PHCA for
sentences. This yields that (i) the
definable functions of
are the polytime functions, and (ii) the
definable functions of
are the functions in the polynomial time hierarchy.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00153-011-0238-7</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Archive for mathematical logic, 2011-07, Vol.50 (5-6), p.643-660 |
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| language | eng |
| recordid | cdi_proquest_miscellaneous_889403493 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Archives Arithmetic Hierarchies Mathematical analysis Mathematical functions Mathematical logic Mathematical Logic and Foundations Mathematical models Mathematics Mathematics and Statistics Original Article Polynomials Sentences |
| title | Admissible closures of polynomial time computable arithmetic |
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