If Σ is any standard formal system adequate for recursive number theory, a formula (having a certain integer q as its Gödel number) can be constructed which expresses the proposition that the formula with Gödel number q is provable in Σ. Is this formula provable or independent in Σ? [2].One approach to this problem is discussed by Kreisel in [4]. However, he still leaves open the question whether the formula (Ex)(x, a), with Gödel-number a, is provable or not. Here (x, y) is the number-theoretic predicate which expresses the proposition that x is the number of a formal proof of the formula with Gödel-number y.In this note we present a solution of the previous problem with respect to the system Zμ [3] pp. 289–294, and, more generally, with respect to any system whose set of theorems is closed under the rules of inference of the first order predicate calculus, and satisfies the subsequent five conditions, and in which the function (k, l) used below is definable.The notation and terminology is in the main that of [3] pp. 306–326, viz. if is a formula of Zμ containing no free variables, whose Gödel number is a, then ({}) stands for (Ex)(x, a) (read: the formula with Gödel number a is provable in Zμ); if is a formula of Zμ containing a free variable, y say, ({}) stands for (Ex)(x, g(y)}, where g(y) is a recursive function such that for an arbitrary numeral the value of g() is the Gödel number of the formula obtained from by substituting for y in throughout. We shall, however, depart trivially from [3] in writing (), where is an arbitrary numeral, for (Ex){x, ).

ABSTRACr Hand tremor due to industrial exposure to metallic mercury vapour was recorded in 26 exposed and 25 non-exposed male workers by an accelerometer attached to the dorsum of the hand. The subjects were instructed to hold the hand and the forearm in the same position first without and then with a load of 1250 g supported by the hand. Analysis of the records showed that the highest peak frequencies (HPF) (the frequency corresponding to the highest acceleration) were higher in the exposed men than in the controls and were related to the duration of exposure to mercury and to age. The changes in HPF between rest and load were again higher in the exposed men than in the controls and again related to the duration of exposure and to age. The second moment (M2) (an index taking into account the whole recorded spectrum) was similar in the exposed men and controls at rest. The changes in M2 between rest and load were higher in the exposed men than in the controls but were related to duration of exposure and to the-biological measurements (loge of mercury in urine or blood) and not to age. These neurophysiological impairments might result from the tendency of metallic mercury to accumulate in the cerebellum and the basal ganglia. These results are consistent with the hypothesis that metallic mercury, even at concentrations probably below the current TLV-TWA of 0 05 mg/m3, can lead to neurological disorders.The most consistent and pronounced effects of exposure to elemental mercury vapour are on the central nervous system (CNS). The first group of effects consists of a neuropsychiatric complex known as "erethism," which includes insomnia, loss of appetite, excessive shyness, and emotional instability.

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. Simple method to determine the efficiency of a cream used for skin protection against solvents. Most of the industrial organic solvents coming into contact with the skin are absorbed through it and enter the blood. They can then be detected in the breath, the analysis of which makes it easy to evaluate skin absorption. Such an evaluation can be made with and without the use of a skin protective (barrier) cream. A comparison of the results allows the efficiency of the cream to be tested.An example of the application of this method is described. The solvent was toluene and the cream tested was composed mainly of talc, glycerol, and water. Ten male volunteers exposed their hands to liquid toluene for 10 minutes. The elimination of the solvent was followed by breath analysis up to 3 hours after the exposure. Two or more sets of exposure were made under different conditions with and without the protective cream.The results show a good standard of efficiency when the cream is carefully and deeply applied. The efficiency of the cream was determined by testing the difference between the decay curves obtained with and without the barrier cream. A relative efficiency was estimated as a percent diminution of solvent excretion by taking the excretion after exposure of unprotected skin as 100%.It is shown that skin absorption for toluene compared with lung absorption may be important and has to be estimated where total exposure is concerned. The method devised here appears to offer simplicity. It is presented as a laboratory test to show the intrinsic value of the cream but its applicability in the field is also considered.

Some syntactically simple fragments of intuitionistic logic possess considerable expressive power compared with their classical counterparts.In particular, we consider in this paper intuitionistic second order propositional logic (ISPL) a formalisation of which may be obtained by adding to the intuitionistic propositional calculus quantifiers binding propositional variables together with the usual quantifier rules and the axiom scheme (Ex), where is a formula not containing x.The main purpose of this paper is to show that the classical first order predicate calculus with identity can be (isomorphically) embedded in ISPL.It turns out an immediate consequence of this that the classical first order predicate calculus with identity can also be embedded in the fragment (PLA) of the intuitionistic first order predicate calculus whose only logical symbols are → and (.) (universal quantifier) and the only nonlogical symbol (apart from individual variables and parentheses) a single monadic predicate letter.Another consequence is that the classical first order predicate calculus can be embedded in the theory of Heyting algebras.The undecidability of the formal systems under consideration evidently follows immediately from the present results.We shall indicate how the methods employed may be extended to show also that the intuitionistic first order predicate calculus with identity can be embedded in both ISPL and PLA.For the purpose of the present paper it will be convenient to use the following formalisation (S) of ISPL based on [3], rather than the one given above.