The aim of this paper is to investigate the area spectrum of the three-dimensional Godel black hole by using two different methods. The result shows that the area spectrum of the black hole is △A = 8πl2p, which conf...The aim of this paper is to investigate the area spectrum of the three-dimensional Godel black hole by using two different methods. The result shows that the area spectrum of the black hole is △A = 8πl2p, which confirms the initial proposal of Bekenstein that the area spectrum is independent of black hole parameters and the spacing is 8πl2p.展开更多
If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） ...If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） are blocked. In these standard accounts （Godel＇s own paper and the exposition in Boolos＇ Computability and Logic are treated as exemplars）, it is assumed that certain formulas （notably so called ＂Godel sentences＂） containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term ＂provable＂ （and indeed ＂unprovable＂） favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.展开更多
基金Project supported by the Scientific Research Foundation of the Education Department of Liaoning Province, China （Grant No. L2011195）.
文摘The aim of this paper is to investigate the area spectrum of the three-dimensional Godel black hole by using two different methods. The result shows that the area spectrum of the black hole is △A = 8πl2p, which confirms the initial proposal of Bekenstein that the area spectrum is independent of black hole parameters and the spacing is 8πl2p.
文摘If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） are blocked. In these standard accounts （Godel＇s own paper and the exposition in Boolos＇ Computability and Logic are treated as exemplars）, it is assumed that certain formulas （notably so called ＂Godel sentences＂） containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term ＂provable＂ （and indeed ＂unprovable＂） favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.
